In the books

In the A Song of Ice and Fire novels, Rhaena was the second daughter of King Aegon III. She's described as a feminine beauty, soft and sweet, more rounded than her two sisters. She loved lace and gold trim and often embroidered depictions of faith on her clothing. She had silver-gold hair, more gold than silver. Unlike Daena and Elaena, she never chaffed at their confinement. She was heavily influenced by her brother, eventually becoming a septa of the Faith of the Seven.

Aegon III's daughter Rhaena was actually at least the third member of House Targaryen to bear that name, because names often repeat in dynasties. The other two Rhaenas have not yet been introduced into the TV continuity. The first Rhaena was a sister of Jaehaerys I, who was forced to marry her half-uncle Maegor the Cruel after he killed her current husband (her brother Aegon). The second Rhaena was Aegon III's own half-sister, called "Rhaena of Pentos". They both shared the same father, Daemon Targaryen, but had different mothers.